**Author(s):**Rita Giuliano Antonini | Milan Paštéka

**Journal:**Uniform Distribution Theory

ISSN 1336-913X

**Volume:**1;

**Issue:**1;

**Start page:**87;

**Date:**2006;

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**Keywords:**Matrix limitation method | Toeplitz matrix | Riesz matrix | weighted density | asymptotic density | permutation of integers | Lévy group of permutations

**ABSTRACT**

A comparison Theorem for matrix limitation methods is proved and the following applications are given: paroindent - new results concerning the comparison between weighted densities generated by different weights; paroindent - new results concerning the comparison between weighted densities of a set $E\subseteq \mathbb N^*$ and those of its transformed set $\pi(E)$, where $\pi$ is a given injective function $\mathbb N^* \to \mathbb N^*$. In particular, a new class of permutations preserving the asymptotic density is identified.